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I would to know why Convolutional Neural Network(CNN) works. It is known from Universal Approximation Theorem that a feedfoward neural network with a single layer can approximate continuous functions. But when it comes to multiple layers, why does it work? Is there a mathematical proof that guarantees this? Please suggest some references if there is any. Thank you very much.

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I don't know the mathematical proof of why it works. However, CNNs are inspired by the layered structure of mammalian visual cortex based on studies of Hubel and Wiesel (1968) in which the understanding of a scenery occurs through a hierarchical construction of images at different levels of abstraction from simple primitive feature extraction in earlier layers to more complex and expressive high-level contextual features in the later layers (Aggarwal, 2018).

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